My Math Forum Confidence Interval -- conceptual understanding

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 March 14th, 2015, 10:16 PM #1 Newbie   Joined: Nov 2014 From: math Posts: 27 Thanks: 1 Confidence Interval -- conceptual understanding In a randomly selected sample of 500 registered voters in Kowloon, 200 individuals say that they plan to vote for Candidate A in the upcoming election. - If the survey were repeated a lot of times, we expect 90% of the confidence intervals constructed will contain the proportion of all Kowloon voters who plan to vote for Candidate A. - If the survey were repeated a lot of times, we expect 90% of the confidence intervals constructed will contain 40%, which is the estimate of the proportion of Kowloon voters who vote for Candidate A. I think the second statement is right, but I was wrong. Why? What's the difference between the two?
 March 15th, 2015, 01:49 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 40% is an estimate of the proportion, but it is not necessarily the true proportion.
 March 15th, 2015, 08:27 PM #3 Newbie   Joined: Nov 2014 From: math Posts: 27 Thanks: 1 Does that mean when we do the survey many times, it is expected that the intervals we get will be the true proportion?
 March 16th, 2015, 03:52 PM #4 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 One of the basic theorems in probability theory is the law of large numbers, which says (essentially) that a sample average converges to the mean as the sample size gets bigger.

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